By: nklein

nklein — Fri, 13 Apr 2007 14:51:10 +0000

Here are some snippets of Smalltalk code that one could add to the Integer class to compute the numbers in the Graham number sequence. And, since Smalltalk already uses arbitrary-precision integers, you should be down the road:

graham
self < 1
ifTrue: [ self error: 'Only supports positive graham indexes.' ].
self = 1
ifTrue: [ ^ 3 arrow: 3 arrowCount: 4. ].
^ 3 arrow: 3 arrowCount: ( ( self-1 ) graham ).

and then the arrow notation method:

arrow: power arrowCount: count
power < 0
ifTrue: [ self error: 'Negative power is a problem.'. ].
count < 1
ifTrue: [ self error: 'Must have at least one arrow.'. ].
power = 0
ifTrue: [ ^ 1. ].
count = 1
ifTrue: [ ^ self * ( self arrow: (power-1) arrowCount: count ). ].
^ self arrow: ( self arrow: (power-1) arrowCount: count ) arrowCount: (count-1).

So, to get the first graham number, one would do: 1 graham. However, you best be able to interrupt it, because even the first number in the series is immense.
Anyhow, that’s 16 lines of code… 6 of which are error checking.

By: rmjarvis

rmjarvis — Fri, 13 Apr 2007 14:43:25 +0000

Here is a C progam that would print out Graham’s number if it could store infinitely large integers:

#include

int f(int a, int b, int c)
{
int i,x;
if(c==1) for(x=1;b>0;–b) x *= a;
else {
x = f(a,b,–c);
for(i=c;i>0;–i) x = f(a,x,c);
}
return x;
}

int g(int n)
{
return n==1 ? f(3,3,4) : f(3,3,g(n-1));
}

int main()
{
return printf(”%d\n”,g(64));
}

Basically, g(n) is the nth number in Graham’s sequence, for which g(64) is Graham’s number. f(a,b,c) is a^^^…^^^b where there are c ^’s in there.

It’s probably a bit longer than the Fortran version, since C doesn’t have any native integer exponent function, so I had to write my own (the c==1 case at the start of the f function.)

Comments on: Follow-up: Graham’s Number

By: nklein

By: rmjarvis